In fact-- click on all of them. You should be able to understand why wrong answers are wrong as well as why right answers are right. A useful exercise, and possible test question, is to ask yourself how you would explain why a given answer is wrong.
After doing a few of these, you will find it easy to make up your own examples.
SERVER
Forehand Backhand
Forehand 9,1 0,10
RECEIVER
Backhand 0,10 6,4
This game is like the Tennis Game in Dixit and Nalebuff, except that if the Receiver is surprised, he never succeeds in returning the serve.
1_1 What is the Nash equilibrium probability of Forehand for the Server?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
1_2 What is the Nash equilibrium probability of Forehand for the Receiver?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
SERVER
Forehand Backhand
Forehand 90,1 0,10
RECEIVER
Backhand 0,10 6,4
The idea in this game is to see what happens to Game 1 when one payoff- (9,1)-- is drastically changed-- to (90,1). It's not tennis anymore, but let's see what happens.
2_1 What is the Nash equilibrium probability of Forehand for the Server?
A. Zero.
B. More than 0 but less than or equal to .2
C. Greater than .2 but less than .5.
D. Between .5 and .7, inclusive
E. Greater than .7
2_2 What is the Nash equilibrium probability of Forehand for the Receiver?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
PAUPER
Work Loaf
Aid 3,2 -1,3
GOVERNMENT
No Aid -1,1 0,0
``The Welfare Game'' models a government that wishes to aid a pauper if
he searches for work but not otherwise, and a pauper who searches for
work only if he cannot depend on government aid. This is a well-known problem in public policy, called ``The Samaritan's Dilemma''
by Tullock (1983, p. 59), who attributes it to James Buchanan. I use it in Chapter 3 of Games and Information . The same problem arises on a private level when parents decide how much to help a lazy child.
3_1 What is the Nash equilibrium probability of Aid for the Government?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
3_2 What is the Nash equilibrium probability of Work for the Pauper?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
BIRD 2
Hawk Dove
Hawk -2, -2 4,0
BIRD 1
Dove 0,4 1,1
This is like the Hawk-Dove Game we looked at in class, except I have changed the numbers so that while the ordinal rankings are the same, Hawks do much better when they meet Doves. (I changed 0,2 to 0,4; and 2,0, to 4,0).
4_1 What is the mixed-strategy Nash equilibrium probability of Hawk for Bird 1?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
4_2 What is the mixed-strategy Nash equilibrium probability of Hawk for Bird 2?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
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